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Published September 1, 2016 | public
Journal Article Open

Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods


In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related methods and is not intended to be comprehensive. We present a general adaptive multiscale model reduction framework, the Generalized Multiscale Finite Element Method. Besides the method's basic outline, we discuss some important ingredients needed for the method's success. We also discuss several applications. The proposed method allows performing local model reduction in the presence of high contrast and no scale separation.

Additional Information

© 2016 Elsevier Inc. Received 15 February 2016. Accepted 27 April 2016. Available online 13 May 2016. YE would like to thank the partial support from the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-FG02-13ER26165 and National Priorities Research Program (NPRP) grant 7-1482-1278 from the Qatar National Research Fund. TYH's research was in part supported by DOE Grant DE-FG02-06ER257, and NSF Grant Nos.DMS-1318377, DMS-1159138. EC's research was in part supported by Hong Kong RGC General Research Fund Project No. 400813.

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August 22, 2023
August 22, 2023